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2 years ago

The midpoint of the segment as an ordered pair (-4,8) (-4,2)

Mathematics

1 answer:

tiny-mole [99]2 years ago

6 0

Answer:

Step-by-step explanation:

(-4,8) & ( -4,2)

$Midpoint=\left(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2} \right)\\\\\\=\left(\dfrac{-4-4}{2},\dfrac{8+2}{2}\right)\\\\\\=\left(\dfrac{-8}{2},\dfrac{10}{2} \right)$

= (-4,5)

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3 years ago

a jogger ran 3 miles due east of his house. then he ran 5 miles at a heading of 30 east of north. how far is he from his house a

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3 years ago

In March, Audrey planted a tomato plant that was 11.25 inches tall. It grew 7.6 inches taller by July. How tall was the tomato s

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3 years ago

Angle A and Angle B are supplementary. Angle A has a measure of 3x - 6 and Angle B has a measure of 54. What is the value of x?

Anni [7]

Answer:

44 degrees

Step-by-step explanation:

Since they are supplementary, they add up to 180. This means that

3x - 6 + 54 = 180

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2 years ago

"A rectangle has a height of 5 cm and its base is increasing at a rate" of 3/2 cm/min. When its area is 60 cm2, at what rate is

sukhopar [10]

Answer:

The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

Step-by-step explanation:

Dimensions of the rectangle

Height = 5cm

Rate of base = 3/2 cm/min

Area = 60cm^2

We know the area of a rectangle of given by = base* Height

b*h = 60

b*5 = 60

b = 12cm

Applying Pythagoras theorem while drawing a diagonal to the rectangle

$b^2 +h^2 = D^2\\$

$5^2 +12^2 = 13^2$

so our diagonal will be 13cm

Upon differentiating the area of the rectangle we get

b*h = A=60cm^2

using the chain rule of differentiation

h*db/dt + b*dh/dt = 0

b*dh/dt = -h*db/dt

12*dh/dt = -5*3/2

dh/dt = -5/8 cm//min

so the height of the rectangle is decreasing at the rate of -5/8cm/min

now we have all the measurements we need

b = 12 , db/dt = 3/2cm/min

h = 5 , dh/dt = -5/8 cm/min

$b^2 +h^2 = D^2$

Upon differentiating we get

2b*db/dt + 2h*dh/dt = 2D*dD/dt

b*db/dt + h*dh/dt = D*dD/dt

12*3/2 + 5*(-5/8) = 13*dD/dt

18 -25/8 = 13*dD/dt

$\frac{144-25}{8}$ = 13*dD/dt

dD/dt = $\frac{119}{104} cm/min$

Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

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3 years ago